and the \(BV(\Omega )\)  space endowed with the norm \(\Vert q\Vert _{BV}:=\Vert q\Vert _{L^1(\Omega )}+\int _{\Omega }|\nabla q|\)  is a Banach space; see, e.g., [1]}, [2]} for more details. Also, in (REF ), \(\alpha >0\)  is a parameter determining the relative weights of the data-fidelity and TV regularization terms in the objective functional.
